text: """
  Copyright 2013 Steven Diamond
  
  Licensed under the Apache License, Version 2.0 (the "License");
  you may not use this file except in compliance with the License.
  You may obtain a copy of the License at
  
      http://www.apache.org/licenses/LICENSE-2.0
  
  Unless required by applicable law or agreed to in writing, software
  distributed under the License is distributed on an "AS IS" BASIS,
  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  See the License for the specific language governing permissions and
  limitations under the License.
  """
  
  from cvxpy.constraints.constraint import Constraint
  import numpy as np
  
  
  class SOC(Constraint):
      """A second-order cone constraint for each row/column.
  
      Assumes ``t`` is a vector the same length as ``X``'s columns (rows) for
      ``axis == 0`` (``1``).
  
      Attributes:
          t: The scalar part of the second-order constraint.
          X: A matrix whose rows/columns are each a cone.
          axis: Slice by column 0 or row 1.
      """
  
      def __init__(self, t, X, axis=0, constr_id=None):
          # TODO allow imaginary X.
          assert not t.shape or len(t.shape) == 1
          self.axis = axis
          super(SOC, self).__init__([t, X], constr_id)
  
      def __str__(self):
          return "SOC(%s, %s)" % (self.args[0], self.args[1])
  
      @property
      def residual(self):
          t = self.args[0].value
          X = self.args[1].value
          if t is None or X is None:
              return None
          if self.axis == 0:
              X = X.T
          norms = np.linalg.norm(X, ord=2, axis=1)
          zero_indices = np.where(X <= -t)[0]
          averaged_indices = np.where(X >= np.abs(t))[0]
          X_proj = np.array(X)
          t_proj = np.array(t)
          X_proj[zero_indices] = 0
          t_proj[zero_indices] = 0
          avg_coeff = 0.5 * (1 + t/norms)
          X_proj[averaged_indices] = avg_coeff * X[averaged_indices]
          t_proj[averaged_indices] = avg_coeff * t[averaged_indices]
          return np.linalg.norm(np.concatenate([X, t], axis=1) -
                                np.concatenate([X_proj, t_proj], axis=1),
                                ord=2, axis=1)
  
      def get_data(self):
          """Returns info needed to reconstruct the object besides the args.
  
          Returns
          -------
          list
          """
          return [self.axis]
  
      def num_cones(self):
          """The number of elementwise cones.
          """
          return np.prod(self.args[0].shape, dtype=int)
  
      @property
      def size(self):
          """The number of entries in the combined cones.
          """
          # TODO use size of dual variable(s) instead.
          return sum(self.cone_sizes())
  
      def cone_sizes(self):
          """The dimensions of the second-order cones.
  
          Returns
          -------
          list
              A list of the sizes of the elementwise cones.
          """
          cones = []
          cone_size = 1 + self.args[1].shape[self.axis]
          for i in range(self.num_cones()):
              cones.append(cone_size)
          return cones
  
      def is_dcp(self):
          """An SOC constraint is DCP if each of its arguments is affine.
          """
          return all(arg.is_affine() for arg in self.args)
  
      def is_dgp(self):
          return False
  
      # TODO hack
      def canonicalize(self):
          t, t_cons = self.args[0].canonical_form
          X, X_cons = self.args[1].canonical_form
          new_soc = SOC(t, X, self.axis)
          return (None, [new_soc] + t_cons + X_cons)
  